Instructor: Dr. Peter CSIKVARI

Description: The general topic of the course is counting in sparse graphs. The object that we count (approximately) can be almost anything: matchings, independents sets, spanning trees, colorings, homomorphisms... The information that we get about the graph can vary too: we may get the whole graph, or some statistics of the local structure, or the degree sequence, or we can consider a random graph or a finite subgraph of an infinite lattice... The tools that we can use is also of great variety: entropy inequalities, zeros of graph polynomials, correlation inequality and correlation decay, properties of multivari- ate polynomials (stability), Markov chains, graph covers... A preliminary draft of the lecture note can be found at .